Chapter 1, Problem 62E

Alternative version of the Borda count. The following simple variation of the conventional Borda count method is sometimes used: last place is worth 0 points, second to last is worth 1 point, ..., first place is worth $N-1$ points (where $N$ is the number of candidates). Explain why this variation is equivalent to the conventional Borda count described in this chapter (i.e., it produces exactly the same winner and the same ranking of the candidates).